Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(836\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{836}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.iv
\(\chi_{7524}(91,\cdot)\) \(\chi_{7524}(775,\cdot)\) \(\chi_{7524}(1351,\cdot)\) \(\chi_{7524}(1675,\cdot)\) \(\chi_{7524}(1819,\cdot)\) \(\chi_{7524}(2143,\cdot)\) \(\chi_{7524}(2359,\cdot)\) \(\chi_{7524}(2863,\cdot)\) \(\chi_{7524}(3259,\cdot)\) \(\chi_{7524}(3403,\cdot)\) \(\chi_{7524}(3547,\cdot)\) \(\chi_{7524}(3727,\cdot)\) \(\chi_{7524}(3943,\cdot)\) \(\chi_{7524}(4195,\cdot)\) \(\chi_{7524}(4915,\cdot)\) \(\chi_{7524}(5239,\cdot)\) \(\chi_{7524}(5311,\cdot)\) \(\chi_{7524}(5779,\cdot)\) \(\chi_{7524}(5923,\cdot)\) \(\chi_{7524}(6823,\cdot)\) \(\chi_{7524}(6967,\cdot)\) \(\chi_{7524}(7291,\cdot)\) \(\chi_{7524}(7363,\cdot)\) \(\chi_{7524}(7507,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,1,e\left(\frac{4}{5}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{1}{10}\right)\) |